/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "a") :: ["A"(1, 1, 1)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "b") :: ["A"(2, 2, 1)] -(1)-> "A"(1, 1, 1)
          F (TrsFun "c") :: ["A"(1, 1, 1)] -(1)-> "A"(1, 0, 1)
          F (TrsFun "main") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          a(b(x)) -> a(c(b(x)))
          main(x1) -> a(x1)
        2. Weak:
          
        

** Step 1.b:1: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#(b(x)) -> c_1(a#(c(b(x))))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#(b(x)) -> c_1(a#(c(b(x))))
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: a#(b(x)) -> c_1(a#(c(b(x))))
** Step 1.b:3: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#(b(x)) -> c_1(a#(c(b(x))))
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:a#(b(x)) -> c_1(a#(c(b(x))))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: a#(b(x)) -> c_1(a#(c(b(x))))
** Step 1.b:4: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))